Melt butter in small saucepan over low heat; blend in flour until smooth. Gradually add milk, stirring constantly with wire whisk or wooden spoon. Add salt and nutmeg, stirring occasionally, simmer for 5 minutes, or until white sauce is thick. Cool.
Mash feta cheese with a fork and combine with the grated cheese, well beaten eggs, parsley and white sauce.
Butter a 9X13 inch baking pan.
Line with half the pastry sheets, brushing each sheet with butter, and letting them come up the sides of the pan.
Pour in the cheese filling and cover with the remaining pastry sheets, brushing each sheet with butter.
Brush top with remaining butter and, with a sharp knife, score the top sheets into strips about 3 inches wide from one end of the pan to the other. Bake in a moderate oven until golden, about 45 minutes.